25.2 Labor Markets and the PPF

In the first part of the course, we assumed that Chuck had a certain amount of labor available to him, and he chose how to allocate that resource across two different goods: making fish or coconuts. We generated the PPF from this labor constraint: \(L_1(x_1) + L_2(x_2) = \overline L\) Any point along this PPF corresponded to some allocation of labor between the two goods:

[ See interactive graph online at https://www.econgraphs.org/graphs/scarcity/ppf/resource_constraint_ppf_curved ]

While Chuck decided how much of different goods to produce, our assumption about firms is that each firm is producing only a single good. But they’re still competing for the same pool of resources: that is, if we assume labor is the only resource of interest, firms in different output markets (firms producing fish and firms producing coconuts, for example) will all buy labor in a common market.

In Week 8 we derived the labor demand curve for a competitive firm as a function of the wage it has to pay and the price of the goods it is selling. For example, if we have two firms (1 and 2) producing two different goods, firm 1 might have a labor demand curve $L_1^\star(w\ |\ p_1)$ that depends on the market wage $w$ and the price of good 1 $p_1$, while firms in industry 2 might likewise have a labor demand curve given by $L_2^\star(w\ |\ p_2)$. Together, their combined labor demand is given by \(LD(w) = L_1^\star(w\ |\ p_1) + L_2^\star(w\ |\ p_2)\) For simplicity, let’s assume that workers supply labor inelastically: that is, regardless of the wage rate, workers will supply some fixed amount $\overline L$ of labor. This is obviously not true, any more than it’s true that all workers are identical; but it’s a convenient assumption to make, and corresponds with our assumption in our first model that Chuck had a fixed amount of labor to divide between two goods. In that case, the equilibrium wage rate will occur where the demand for labor equals the supply of labor: \(\begin{aligned} LD(w) &= LS(w)\\ L_1^\star(w\ |\ p_1) + L_2^\star(w\ |\ p_2) &= \overline L \end{aligned}\) Note that this is essentially the exact equation for a PPF, with a twist: instead of being functions of $x_1$ and $x_2$, the amount of labor devoted to goods 1 and 2 is determined by the three prices in the model: $p_1$, $p_2$, and $w$.

The following graph shows the individual and market labor demand curves, as well as the labor supply curve:

[ See interactive graph online at https://www.econgraphs.org/graphs/competition/equilibrium/prices_and_individual_and_market_labor_demand ]

You can drag the individual labor demand curves back and forth to simulate shifts in demand. As you can see, if one firm’s labor demand curve increases, it the wage rate increases, causing the other firm to hire fewer workers. The end result is a reallocation of labor from one good to another. Likewise, you can change the labor supplied, $\overline L$, by dragging the orange vertical line back and forth. An increase in the labor supply causes wages to drop and all firms to hire more labor (and, implicitly, produce more goods).

In short, we can think of this model as taking three determinants of the wage rate: $p_1$, $p_2$, and $\overline L$, and determining the equilibrium wage rate, and therefore the equilibrium allocation of labor. Put another way, we can think of these three factors working together to choose a point along the PPF:

[ See interactive graph online at https://www.econgraphs.org/graphs/scarcity/general_equilibrium/resource_constraints_ppf_competitive ]